A known type of electro-optic switch is illustrated schematically in FIG. 1. The switch comprises a pair of optical waveguides 12 and 14 formed in an electro-optic substrate 16 such as lithium niobate. Waveguides 12 and 14 include respective coupling sections 18 and 20 that lie within coupling region 22 of length L. Within coupling region 22, the waveguides are close enough to one another to permit evanescent field coupling between their respective coupling sections 18 and 20. Electrodes 24 and 26 are positioned over coupling sections 18 and 20, respectively, and permit control over the operation of the switch, as described below.
Whthin coupling region 22, an optical signal passing through one waveguide will be coupled into the other waveguide. Regarding one end of waveguide 12 as an input port 32 and the opposite ends of the waveguides as output ports 34 and 36, and optical input signal I appearing at input port 32 will in general have its power divided between the waveguides, such that it produces optical output signals at both output ports. The output signals at output ports 34 and 36 are designated I.sub.0 and I-I.sub.0, respectively. When an optical input signal at input port 32 appears only at output port 34, the optical switch is said to be in a straight-through state. When the optical output signal appears only at output port 36, the switch is said to be in a crossover state. The straight-through and crossover states are symbolized by circles containing equal signs and crosses, respectively, as shown in FIG. 1.
Each particular coupling region between a pair of optical waveguides is characterized by its interaction length L, by a coupling length l.sub.c, and by the difference or mismatch .DELTA..beta. between the propagation constants .beta..sub.1 and .beta..sub.2 of the respective waveguide coupling sections. Assume that two waveguides have equal propagation constants, such that .DELTA..beta.=0. When an optical signal enters the coupling region in a first one of the waveguides, the power of the optical signal will begin transferring from the first waveguide to the second waveguide. After traveling a distance equal to the coupling length l.sub.c, all of the optical power will have transferred to the second waveguide. Thereafter, optical power will begin transferring back to the first waveguide, such that after traveling a total length of 2l.sub.c, all of the optical power will have returned to the first waveguide.
As a result of the above properties, complete crossover can be produced, for waveguides that are exactly phase matched (.DELTA..beta.=0), when the interaction length L is an exact odd multiple of the coupling length l.sub.c. In effect, coupling length l.sub.c is the length of a particular coupling region needed to transfer all of the optical power from one waveguide to the other waveguide, when the waveguides are phased matched. When .DELTA..beta. is not equal to zero, then the transfer of power between the waveguides is more complex, and in general it may be impossible to achieve complete crossover using only a single pair of electrodes.
The device shown in FIG. 1 can be made to operate as an optical switch by applying a voltage to electrodes 24 and 26. Assume that the interaction length L is equal to l.sub.c, and that the waveguides are phase matched (.DELTA..beta.=0) in the absence of an electric field. Under such circumstances, with zero voltage applied to the electrodes, the switch will be in the crossover state, and an input signal at input port 32 will appear only at output port 36, as described above. However, if a differential voltage is applied to electrodes 24 and 26, then the resulting electric field in the coupling region will modify the index of refraction of the electro-optic substrate and of coupling sections 18 and 20, and will whereby produce a phase mismatch .DELTA..beta. between the propagation constants of the waveguides. As a result, the input singal will no longer entirely cross over, and will instead be split between the output ports. By appropriate selection of the voltage applied to the electrodes, the switch can be put in the straight-through state, in which all of the input signal appears at output port 34.
FIG. 2 shows the output signal I.sub.0 at output port 34 as a function of the normalized propagation constant difference .DELTA..beta.L/.pi. between the waveguides. The normalized propagation constant difference is directly proportional to the applied voltage. When the applied voltage and normalized propagation constant difference are equal to zero, the switch will be in the crossover state. However, when the normalized propagation constant difference is equal to .+-..sqroot.3, the switch will be in the straight-through state, and all of the optical power will appear at output port 34 as signal I.sub.0. Thus the appropriate voltage applied to the electrodes can cause the optical input signal to be switched to either output port.
A significant problem with the optical switch shown in FIG. 1 is that very precise control of the voltage applied to the electrodes is required in order to produce switching with acceptably low levels of crosstalk. For example, one needs to apply and maintain voltages that produce a normalized propagation constant difference of between -0.03 and +0.03 for the crossover state, and between 1.69 and 1.77 for the straight-through state, in order to keep crosstalk between the two output ports below the 30 dB level. Other types of prior directional coupler switches, including those with multiple electrode sections within the coupling region, have similarly stringent voltage requirements.